Journal of Multivariate Analysis最新文献

英文中文

Limiting spectral distribution of high-dimensional integrated covariance matrices based on high-frequency data with multiple transactions 基于多事务高频数据的高维积分协方差矩阵的谱限分布

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-28 DOI: 10.1016/j.jmva.2025.105568

Moming Wang , Ningning Xia , Yong Zhou

Due to the heavy trading volume in financial markets and the limitations of recording mechanisms, the occurrence of multiple transactions during each recording period is a common feature of high-frequency data. This paper investigates how the number of such multiple transactions impacts the behavior of an averaged version of time-variation adjusted realized covariance (ATVA) matrix in a high-dimensional situation, where the number of stocks and the observation frequency go to infinity proportionally. By using random matrix theory, we derive the limiting spectral distribution (LSD) of ATVA matrices based on high-frequency multiple observations. We demonstrate how the LSD of ATVA matrices depends on the number of multiple transactions. The study of the LSD of random matrices is not only theoretically interesting in itself but also provides a better insight into the pre-averaging approach, which is widely used to deal with the microstructure noise. Furthermore, we investigate the limits of spiked eigenvalues of ATVA matrices when the covariance matrix of asset prices exhibits a spiked pattern. Finally, the theoretical results are supported by simulation studies.

由于金融市场的大交易量和记录机制的限制，高频数据在每个记录周期内发生多笔交易是高频数据的共同特征。本文研究了在股票数量和观察频率成比例趋近无穷大的高维情况下，这类多重交易的数量如何影响时变调整已实现协方差（ATVA）矩阵的平均版本的行为。利用随机矩阵理论，推导了基于高频多次观测的ATVA矩阵的极限谱分布。我们演示了ATVA矩阵的LSD如何依赖于多个事务的数量。对随机矩阵的LSD的研究不仅在理论上很有意义，而且对广泛应用于微观结构噪声处理的预平均方法提供了更好的理解。此外，我们研究了当资产价格的协方差矩阵呈现出尖峰模式时，ATVA矩阵的尖峰特征值的极限。最后，通过仿真研究对理论结果进行了验证。

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引用次数: 0

Threshold models for high-dimensional time series with network structure 具有网络结构的高维时间序列阈值模型

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-28 DOI: 10.1016/j.jmva.2025.105560

Chi Tim Ng , Chun Yip Yau , Yuanbo Li , Lei Qin

Threshold autoregressive (TAR) models form an important class of nonlinear time series models and have attracted great attentions in the literature. In order to extend threshold modeling to high-dimensional nonlinear time series, a threshold network autoregressive (TNAR) model is proposed in this paper to overcome the difficulty of over-parameterization by exploiting the available information of network relations. The proposed model can characterize the regime-switching feature in nonlinear complex network systems. Sufficient conditions for the strict stationarity and the ergodicity of the TNAR model are established. A computationally efficient method based on group LASSO is developed to estimate the multiple thresholds and the parameters. A grouped TNAR model is also proposed to further reduce the number of the parameters. The asymptotic behavior of the proposed method is explored and the estimation consistency of both number of groups and group membership structure is established.

阈值自回归（TAR）模型是一类重要的非线性时间序列模型，一直受到文献的广泛关注。为了将阈值建模推广到高维非线性时间序列，利用网络关系的可用信息，提出了一种阈值网络自回归（TNAR）模型，克服了过度参数化的困难。该模型可以表征非线性复杂网络系统的状态切换特征。建立了TNAR模型的严格平稳性和遍历性的充分条件。提出了一种基于群LASSO的快速估计多阈值和参数的方法。为了进一步减少参数的数量，还提出了分组TNAR模型。研究了该方法的渐近性，建立了群数和群隶属结构的估计一致性。

引用次数: 0

Robust bilinear factor analysis based on the matrix-variate t distribution 基于矩阵变量t分布的稳健双线性因子分析

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-28 DOI: 10.1016/j.jmva.2025.105575

Xuan Ma , Jianhua Zhao , Changchun Shang , Fen Jiang , Philip L.H. Yu

Factor Analysis based on the multivariate t distribution (tFA) is a useful robust tool for extracting common factors on heavy-tailed or contaminated data. However, tFA is only applicable to vector data. When tFA is applied to matrix data, it is common to first vectorize the matrix observations. This introduces two challenges for tFA: (i) the inherent matrix structure of the data is broken, and (ii) robustness may be lost, as vectorized matrix data typically results in a high data dimension, which could easily lead to the breakdown of tFA. To address these issues, starting from the intrinsic matrix structure of matrix data, a novel robust factor analysis model, namely bilinear factor analysis built on the matrix-variate t distribution (tBFA), is proposed in this paper. The novelty is that it is capable of simultaneously extracting common factors for both row and column variables of interest on heavy-tailed or contaminated matrix data. Two efficient algorithms for maximum likelihood estimation of tBFA are developed. Closed-form expressions for the Fisher information matrix to calculate the accuracy of parameter estimates are derived. Empirical studies are conducted to understand the proposed tBFA model and compare it with related competitors. The results demonstrate the superiority and practicality of tBFA. Importantly, tBFA exhibits a significantly higher breakdown point than tFA, making it more suitable for matrix data.

基于多元t分布（tFA）的因子分析是提取重尾或污染数据的共同因子的一种有用的鲁棒工具。然而，tFA仅适用于矢量数据。当tFA应用于矩阵数据时，通常首先对矩阵观测值进行矢量化。这给tFA带来了两个挑战：(i)数据固有的矩阵结构被打破，（ii）鲁棒性可能会丧失，因为矢量化的矩阵数据通常会导致高数据维数，这很容易导致tFA的崩溃。为了解决这些问题，本文从矩阵数据的固有矩阵结构出发，提出了一种新的鲁棒因子分析模型，即基于矩阵变量t分布的双线性因子分析（tBFA）。新颖之处在于，它能够同时提取重尾或污染矩阵数据上感兴趣的行和列变量的公共因子。提出了两种有效的tBFA最大似然估计算法。导出了计算参数估计精度的费雪信息矩阵的封闭表达式。通过实证研究来理解所提出的tBFA模型，并将其与相关竞争对手进行比较。结果表明了tBFA的优越性和实用性。重要的是，tBFA比tFA具有更高的击穿点，使其更适合于矩阵数据。

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引用次数: 0

Estimation of tensor factor model by iterative least squares 张量因子模型的迭代最小二乘估计

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-28 DOI: 10.1016/j.jmva.2025.105557

Yong He , Yujie Hou , Yalin Wang , Wen-Xin Zhou

For large-dimensional tensor time series, dimension reduction plays a pivotal role. Tensor factor model depicts tensor-valued time series through a low-dimensional projection on a space of common factors, thereby achieving great dimension reduction and having a wide range of applications in economics and finance. In this paper, we propose a simple iterative least squares algorithm for estimating tensor factor model. We first estimate the latent common factors by using deterministic mode-

k

projection matrices and then estimate the loading matrices by minimizing the squared Frobenius loss function under certain identifiability conditions. The estimated loading matrices are further taken as new mode-

k

projection matrices, and the above update procedures are iteratively executed until convergence. We also propose a novel eigenvalue ratio method for estimating the number of factors and show the consistency of the estimators. Given the true number of factors, we theoretically establish the convergence rates of the estimated loading matrices and signal components at the

s

th iteration for any

s \geq 1

. Thorough numerical studies are conducted to investigate the finite-sample performance of the proposed method. Analyses of import-export transport networks and lung cancer histopathological image datasets illustrate the empirical usefulness of the proposed method.

对于大维张量时间序列，降维起着至关重要的作用。张量因子模型通过在公共因子空间上的低维投影来描述张量值时间序列，从而实现了极大的降维，在经济和金融领域有着广泛的应用。本文提出了一种简单的迭代最小二乘算法来估计张量因子模型。首先利用确定性模式k投影矩阵估计潜在的公共因子，然后在一定的可辨识性条件下，通过最小化Frobenius损失函数的平方来估计加载矩阵。将估计的加载矩阵作为新的k型投影矩阵，迭代执行上述更新过程直至收敛。我们还提出了一种新的估计因子数量的特征值比方法，并证明了估计量的一致性。在给定因子的真实数目的情况下，我们从理论上建立了对任意s≥1的估计加载矩阵和信号分量在第5次迭代时的收敛速率。对该方法的有限样本性能进行了深入的数值研究。对进出口运输网络和肺癌组织病理学图像数据集的分析说明了所提出方法的经验有效性。

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引用次数: 0

Symmetric Bernoulli distributions and minimal dependence copulas 对称伯努利分布和最小依赖公式

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-17 DOI: 10.1016/j.jmva.2025.105545

Alessandro Mutti, Patrizia Semeraro

The key result of this paper is to characterize all multivariate symmetric Bernoulli distributions whose sum is minimal under the convex order. In doing so, we automatically characterize extremal negative dependence among Bernoulli variables, since multivariate distributions with minimal convex sums are known to be strongly negative dependent. Moreover, beyond its interest per se, this result provides insight into negative dependence within the class of copulas. In particular, two classes of copulas can be built from multivariate symmetric Bernoulli distributions: extremal mixture copulas and FGM copulas. We analyze the extremal negative dependence structures of copulas constructed from symmetric Bernoulli vectors with minimal convex sums and explicitly find a class of minimal dependence copulas. This analysis is completed by investigating minimal pairwise dependence measures and correlations. Our main results derive from the geometric and algebraic representations of multivariate symmetric Bernoulli distributions, which effectively encode key statistical properties.

本文的关键结果是刻画了凸阶下和最小的所有多元对称伯努利分布。在这样做时，我们自动表征伯努利变量之间的极值负相关，因为已知最小凸和的多元分布是强负相关的。此外，除了其本身的兴趣之外，该结果还提供了对copulas类内负依赖的见解。特别地，可以从多元对称伯努利分布中建立两类copula：极值混合copula和FGM copula。本文分析了具有最小凸和的对称伯努利向量的极负相关结构，明确地找到了一类最小相关的copula。该分析是通过调查最小两两依赖度量和相关性来完成的。我们的主要结果来自多元对称伯努利分布的几何和代数表示，它有效地编码了关键的统计性质。

引用次数: 0

Recent advances in principal component analysis for directional data 定向数据主成分分析的新进展

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-15 DOI: 10.1016/j.jmva.2025.105528

Anahita Nodehi , Meisam Moghimbeygi , Christophe Ley

The high dimensionality of the input data can pose multiple problems when implementing statistical techniques. The presence of many dimensions in the data can lead to challenges in visualizing the data, higher computational demands, and a higher probability of over-fitting or under-fitting in modeling. Furthermore, the curse of dimensionality contributes to these issues by stating that the necessary number of observations for accurate modeling increases exponentially as the number of dimensions increases. Dimension reduction tools help overcome this challenge. Principal Component Analysis (PCA) is the most widely used technique, intensively studied in classical linear spaces. However, in applied sciences such as biology, bioinformatics, astronomy and geology, there are many instances in which the data’s support are non-Euclidean spaces. In fact, the available data often include elements of Riemannian manifolds such as the unit circle, torus, sphere, and their extensions. Therefore, the terms “manifold-valued” or “directional” data are used in the literature for these situations. When dealing with directional data, the linear nature of PCA might pose a challenge to achieve accurate data reduction. This paper therefore reviews and investigates the methodological aspects of PCA on directional data and their practical applications.

在实现统计技术时，输入数据的高维可能会带来多个问题。数据中存在许多维度可能会导致数据可视化的挑战，更高的计算需求，以及建模中过度拟合或欠拟合的更高概率。此外，维度的诅咒通过指出精确建模所需的观测数量随着维度数量的增加而呈指数增长来促成这些问题。降维工具有助于克服这一挑战。主成分分析（PCA）是应用最广泛的技术，在经典线性空间中得到了深入的研究。然而，在诸如生物学、生物信息学、天文学和地质学等应用科学中，有许多情况下数据的支持是非欧几里得空间。事实上，可用的数据通常包括黎曼流形的元素，如单位圆、环面、球体及其扩展。因此，术语“流形值”或“定向”数据在这些情况下的文献中使用。在处理方向数据时，主成分分析的线性特性可能会对实现准确的数据约简提出挑战。因此，本文回顾和探讨了主成分分析在定向数据上的方法学方面及其实际应用。

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引用次数: 0

Asymptotics for a discounted systemic risk measure in a multi-dimensional risk model with dependent claim sizes and stochastic return 具有独立索赔规模和随机收益的多维风险模型中贴现系统风险测度的渐近性

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-28 DOI: 10.1016/j.jmva.2025.105569

Yang Yang , Zhenyuan Xu , Yahui Fan

Consider a multi-dimensional renewal risk model, in which an insurer simultaneously operates more than one line of business, and is allowed to make both risk-free and risky investments. The claim sizes from all business lines are triggered by a series of common shocks, whose arrival times constitute a renewal counting process. The price process of the investment portfolio is described as a geometric Lévy process. In this study, we consider two cases that the claim sizes from different business lines are asymptotically dependent or asymptotically independent. Under the framework of regular variation, we study the asymptotic behavior of a discounted systemic risk measure, which is proposed by Li (2022) to describe the instant expected shortfall of the insurer at the moment when one of its business lines suffers crisis. The obtained results indicate that the asymptotics for the discounted systemic risk measure depend on neither the price process of the investment nor the renewal shock-number process, and, in addition, the asymptotic independence also gives no contribution to the asymptotic formula.

考虑一个多维续保风险模型，在该模型中，保险公司同时经营多条业务线，并允许进行无风险和有风险的投资。来自所有业务线的索赔大小由一系列常见冲击触发，其到达时间构成续期计数过程。投资组合的价格过程被描述为一个几何lsamvy过程。在本研究中，我们考虑了两种情况，即来自不同业务线的索赔规模是渐近相关的或渐近独立的。在规则变化的框架下，我们研究了Li（2022）提出的贴现系统风险测度的渐近行为，该测度描述了当保险公司的一条业务线遭受危机时的即时预期缺口。所得结果表明，贴现系统风险测度的渐近性既不依赖于投资价格过程，也不依赖于更新冲击数过程，而且渐近独立性对渐近公式也没有贡献。

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引用次数: 0

Uniform designs for experiments with branching and nested factors 具有分支和嵌套因素的实验的统一设计

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-12-01 DOI: 10.1016/j.jmva.2025.105576

Feng Yang , Zheng Zhou , Yongdao Zhou

The factors that exist only at certain levels of other factors are called the nested factors. The factors that lead to such nested factors are called the branching factors. Experiments with branching and nested factors occur frequently in practical applications. Designing such experiments is challenging due to the special relationship between the branching and nested factors. In this paper, we propose uniform designs for experiments involving branching and nested factors. A novel criterion is introduced to measure the uniformity of such designs, and the corresponding lower bound is also given. The construction methods of uniform designs for experiments with branching and nested factors are provided, and their effectiveness is verified by simulation comparisons and a practical manufacturing experiment. The proposed method allows each of branching, nested and shared factors to be either qualitative or quantitative. Moreover, the run size and the levels of quantitative factors are very flexible, such that our method works well for both physical and computer experiments.

只存在于其他因素的一定水平上的因素称为嵌套因素。导致这些嵌套因子的因子被称为分支因子。分支因子和嵌套因子的实验在实际应用中经常出现。由于分支和嵌套因素之间的特殊关系，设计这样的实验是具有挑战性的。在本文中，我们提出了涉及分支和嵌套因素的实验的统一设计。引入了一种新的准则来衡量这种设计的均匀性，并给出了相应的下界。给出了分支因子和嵌套因子实验均匀设计的构建方法，并通过仿真对比和实际制造实验验证了其有效性。所提出的方法允许每个分支、嵌套和共享的因素是定性的或定量的。此外，运行规模和定量因素的水平非常灵活，因此我们的方法对物理和计算机实验都很有效。

引用次数: 0

Estimation for partially time-varying spatial autoregressive panel data model under linear constraints 线性约束下部分时变空间自回归面板数据模型的估计

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-19 DOI: 10.1016/j.jmva.2025.105547

Lingling Tian , Chuanhua Wei , Bing Sun , Mixia Wu

This paper investigates a constrained spatial autoregressive panel data model with fixed effects, partially linear time-varying coefficients, and time-varying spatial dependence. We propose a constrained profile two-stage least squares estimator and establish its asymptotic properties. Furthermore, a statistical test is constructed to examine whether the constant coefficients satisfy pre-specified linear constraints. Monte Carlo simulations under both independent and

α

-mixing error structures demonstrate the finite-sample performance of the proposed estimators and testing procedure. A real data example is provided to illustrate the practical applicability of the method. In addition, when the time dimension

T

is relatively small, a Block Bootstrap procedure is proposed to compute the

p

-value for the test.

本文研究了具有固定效应、部分线性时变系数和时变空间依赖性的约束性空间自回归面板数据模型。提出了一种约束轮廓两阶段最小二乘估计，并建立了它的渐近性质。此外，构造了一个统计检验来检验常系数是否满足预先规定的线性约束。在独立误差结构和α-混合误差结构下的蒙特卡罗模拟验证了所提估计器和测试方法的有限样本性能。通过一个实际的数据算例说明了该方法的实用性。此外，当时间维T较小时，提出了Block Bootstrap方法来计算检验的p值。

引用次数: 0

A componentwise estimation procedure for multivariate location and scatter: Robustness, efficiency and scalability 多变量定位和分散的组件估计方法：鲁棒性、效率和可扩展性

IF 1.4 3区数学 Q2 STATISTICS & PROBABILITY

Journal of Multivariate Analysis

Pub Date : 2026-03-01 Epub Date: 2025-11-19 DOI: 10.1016/j.jmva.2025.105546

Soumya Chakraborty , Ayanendranath Basu , Abhik Ghosh

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model misspecification and the presence of outliers in the data; on the other hand robust estimators with reasonably high efficiency are often computationally challenging for modern large and complex datasets. In this work, we propose a new, simple, robust and highly efficient method for estimation of the location vector and the scatter matrix for elliptically symmetric distributions. The proposed estimation procedure is designed in the spirit of the minimum density power divergence (DPD) estimation approach with appropriate modifications which makes our proposal (componentwise minimum DPD estimation) computationally very economical and scalable to large as well as higher dimensional datasets. Consistency and asymptotic normality of the proposed componentwise estimators of the multivariate location and scatter are established along with asymptotic positive definiteness of the estimated scatter matrix. Robustness of our estimators are studied by means of influence functions. All theoretical results are illustrated further under multivariate normality. A large-scale simulation study is presented to assess finite sample performances and scalability of our method in comparison to the usual maximum likelihood estimator (MLE), the ordinary minimum DPD estimator (MDPDE) and other popular non-parametric methods. The applicability of our method is further illustrated with a real dataset on credit card transactions.

协方差矩阵估计是多变量数据分析中的一个重要问题，无论从理论还是应用的角度来看都是如此。众所周知，许多简单和流行的协方差矩阵估计受到模型不规范和数据中存在异常值的严重影响；另一方面，对于现代大型和复杂的数据集，具有相当高效率的鲁棒估计器通常在计算上具有挑战性。在这项工作中，我们提出了一种新的，简单，鲁棒和高效的方法来估计椭圆对称分布的位置向量和散点矩阵。所提出的估计程序是根据最小密度功率散度（DPD）估计方法的精神设计的，并进行了适当的修改，这使得我们的建议（组件最小DPD估计）在计算上非常经济，并且可扩展到大型和高维数据集。建立了多元位置和散点的分量估计的一致性和渐近正态性，以及估计的散点矩阵的渐近正定性。利用影响函数研究了估计量的鲁棒性。所有理论结果在多元正态性下得到进一步说明。通过大规模的仿真研究，与常用的极大似然估计器（MLE）、普通最小DPD估计器（MDPDE）和其他流行的非参数方法相比，评估了该方法的有限样本性能和可扩展性。通过信用卡交易的真实数据集进一步说明了我们方法的适用性。

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